US4731863A - Digital image processing method employing histogram peak detection - Google Patents
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- 238000001514 detection method Methods 0.000 title claims abstract description 38
- 238000003672 processing method Methods 0.000 title claims abstract description 17
- 238000000034 method Methods 0.000 claims abstract description 32
- 238000009499 grossing Methods 0.000 claims abstract description 10
- 230000006870 function Effects 0.000 claims description 36
- 210000000038 chest Anatomy 0.000 claims description 15
- 210000004072 lung Anatomy 0.000 claims description 15
- 210000001370 mediastinum Anatomy 0.000 claims description 14
- 230000001186 cumulative effect Effects 0.000 claims description 11
- 238000005315 distribution function Methods 0.000 claims description 11
- 238000000926 separation method Methods 0.000 claims description 6
- 238000012935 Averaging Methods 0.000 claims 3
- 238000002601 radiography Methods 0.000 description 5
- 210000003484 anatomy Anatomy 0.000 description 4
- 230000003247 decreasing effect Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- OAICVXFJPJFONN-UHFFFAOYSA-N Phosphorus Chemical compound [P] OAICVXFJPJFONN-UHFFFAOYSA-N 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000001627 detrimental effect Effects 0.000 description 1
- 238000003709 image segmentation Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 230000003902 lesion Effects 0.000 description 1
- 238000007781 pre-processing Methods 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
- 238000010187 selection method Methods 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
- 238000009987 spinning Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N5/00—Details of television systems
- H04N5/30—Transforming light or analogous information into electric information
- H04N5/32—Transforming X-rays
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/11—Region-based segmentation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/10—Segmentation; Edge detection
- G06T7/136—Segmentation; Edge detection involving thresholding
Definitions
- This invention relates to the field of digital image processing, and more particularly to a method for processing a digital image to automatically detect peaks in a gray-level histogram of the digital image.
- a knowledge of the location of the peaks in the histogram is useful in selecting gray level thresholds for segmenting the digital image into distinguishable structures.
- McAdams et al (see “Histogram Directed Processing of Digital Chest Images" by H.P. McAdams et al, Investigative Radiology, March 1986, Vol. 21, pp. 253-259) have discussed anatomical-structure selective image processing as applied to digital chest radiography. They used the lung field and the mediastinum histograms individually to determine a lung/mediastinum gray level threshold. The individual histograms for the lung field and the mediastinum were constructed by a trackball-driven cursor outlining technique. The gray level threshold was selected from the gray levels at which the two histograms overlap. McAdams et al. presented impressive results of anatomical structure-selective image processing guided by a lung/mediastinum gray level threshold.
- the object of the invention is achieved by a digital image processing method for automatically detecting peaks in a gray level histogram of the digital image characterized by applying smoothing and differencing operators to the gray level histogram to generate a peak detection function wherein positive to negative zero crossings in the function represent the start of a peak, and a maximum of the function following such a positive to negative zero crossing represents the end of a peak.
- Gray level thresholds are set at gray levels between the detected peaks.
- FIG. 1 is block diagram showing digital image processing apparatus useful for practicing the digital image processing method of the present invention
- FIG. 2 is a histogram of a typical chest radiograph
- FIG. 3 is a graph showing the cumulative distribution function of the digital image represented by the histogram in FIG. 2;
- FIG. 4 is a graph illustrating the form of the smoothing and differencing operations employed in one mode of practicing the present invention
- FIG. 5 is a graph showing a peak detection function generated by a smoothing window of width 541;
- FIG. 6 is a graph showing the peak detection function generated by a smoothing window of width 271;
- FIG. 7 is an enlarged view of the histogram shown in FIG. 2, illustrating the locations of the detected peaks for a smoothing window of width 541 and 271 respectively;
- FIG. 8 is a flow chart of a generalized peak detection method according to the present invention.
- FIG. 9 is a histogram of a digital radiographic image of human hands.
- FIG. 1 is a schematic diagram illustrating digital image processing apparatus useful for practicing the method of the present invention.
- the apparatus includes a scanning input portion which may comprise, for example, a drum scanner 10 for scanning transparencies such as conventional film radiographs.
- the drum scanner 10 includes a transparent drum 12 on which the radiograph 14 is mounted.
- a light source 16 is provided inside the drum to illuminate a spot on the radiograph.
- a photo sensor 18 receives the light signal modulated by the radiograph 14.
- the drum 12 spins on its axis in the direction of arrow A to form line scans, and the light source and sensor are moved relative to the radiograph in the direction of arrow B to form the scan raster.
- the analog signal detected by the photosensor 18 is amplified by an amplifier 20 and is converted to a digital signal by an analog to digital converter 22.
- the scanning input portion of the digital image processing apparatus may also comprise a stimulable storage phosphor radiographic imaging system of the type shown in U.S. Pat. No. 3,859,257 issued to Luckey, January 1975 reissued as U.S. Pat. No. Re. 31,847, Mar. 12, 1985.
- the digital radiographic signal is stored in a memory 24 and is processed by a digital image processing computer 26.
- the digital image processing computer 26 may comprise a general purpose digital computer, or a special purpose digital computer designed specifically for processing images.
- the digital image processing computer performs operations on a digital image, such as tone scale adjustment, and edge enhancement according to well known digital image processing methods.
- the processed digital image is converted to a video signal by signal processing electronics and video encoder 28 and is displayed on a video monitor 30.
- the digital image is displayed by producing a film image on output scanning apparatus 32.
- the output scanning apparatus comprises a digital to analog converter 34 for converting the processed digital image signal to an analog signal, an amplifier 36 for amplifying the analog image signal, and a light source 38 modulated by the analog signal.
- Light source 38 is focused to a spot by a lens 40 onto a photosensitive medium such as photographic film 42 on a spinning drum 44.
- the various elements of the digital image processing apparatus communicate via a data and control bus 46.
- FIG. 2 is a histogram plot compiled from a typical chest radiograph that was scanned and digitized by apparatus such as shown in FIG. 1.
- the digital image signal was a 12 bit 1250 ⁇ 1400 pixel image.
- FIG. 2 it is not readily apparent from visual observation of the histogram, which cluster of peaks in the histogram belong to the lungs, and which to the mediastinum.
- the plot shown in FIG. 2 is typical of a histogram from a chest radiograph and illustrates the difficulty of selecting a gray level threshold between the lungs and mediastinum.
- the inventors have found, through experimentation, that a gray level threshold between the portions of the histogram representing the lung and mediastinum may be reliably selected by the method of the present invention.
- the method involves the steps of applying smoothing and differencing operations to the histogram to produce a peak detection function wherein a positive to negative zero crossing in the function indicates the beginning of a peak, and a maximum occurring after such a positive to negative crossing represents the end of a peak.
- F(n) is the cumulative distribution function of the gray levels in the image
- the cumulative distribution function F(n) is smoothed by applying a sliding window average having a width w to produce a smoothed cumulative distribution function F w (n).
- the peak detection function r(n) is generated by subtracting the smoothed cumulative distribution function F w (n) from the original cumulative distribution function F(n) as follows:
- the resulting function r(n) is a function having positive to negative zero crossings that correspond to the beginnings of peaks in the histogram, and maxima corresponding to the ends of the peaks in the histograms.
- the peak detection function r(n) can be computed directly from the histogram h(n) by the following convolution
- q w (n) is a function that can be expressed as the convolution of a "smoothing" kernel s w (n) and a “differencing" kernel d(n) as follows:
- FIG. 5 shows the peak detection function r(n) generated from the histogram of FIG. 1 using a smoothing window w, 541 samples wide.
- a i -- is a positive to negative zero crossing, and indicates the gray level at which the ith peak starts
- b i is a maximum after the ith positive to negative zero crossing and indicates the gray level at which the ith peak ends.
- the pair (a i , b i ) characterizes the ith peak detected.
- FIG. 6 shows the peak detection function r(n) generated with a window size w, 271 samples wide.
- p(n)--represents the percentage of the total number of gray levels confined to the interval [o, n] (p(n) 100 F(n))
- n T represents the gray level threshold between the lung and the mediastinum
- d-- is an empirically derived constant representing the minimum separation in gray levels between two clusters of peaks
- n Max -- is the largest gray level present in the image.
- the signal processing method was applied to the digital chest radiograph having the histogram shown in FIG. 2.
- the parameters were set as follows:
- the threshold selection method according to the present invention was applied to an assortment of digital chest radiographs to select gray level thresholds between the lungs and the mediastinum. Then various anatomical structure selective image enhancement procedures were applied to the digital chest radiographs using the selected gray level thresholds.
- the image enhancement procedures included anatomical selective tone scale adjustment and edge enhancement. In these tests, the gray level thresholds automatically selected by the method of the present invention were found to be appropriate and yielded diagnostically useful results.
- Steps 1.7 and 1.8 of the above method exploit the a priori knowledge of the existence of at most two well-separated (at least by d in gray levels) major histogram clusters corresponding to the mediastinum and the lung field.
- images can have any number of major structures each of which correspond to a single, or a group of histogram peaks (clusters).
- the thresholds separating the major structures are then set to gray levels between these peaks.
- the A 2 -intervals (or equivalently the A 2 -peaks), i.e., (c k ,d k )'s may overlap with the A 1 -intervals (or equivalently the A 1 -peaks), i.e., (a i ,b i )'s. If the relative population of the gray levels contained in the overlap exceeds a predetermined value then the overlap is said to be ⁇ significant ⁇ . Nonoverlapping peaks, or insignificantly overlapping peaks are called ⁇ independent ⁇ peaks. The overlapping and the independent peaks are determined by the overlap detection procedure described below.
- the set C of the major peaks is formed via the following rules:
- the final set C can be defined as
- the window sizes w 1 and w 2 and the criteria R maj , and t can be determined empirically for the class of images that is of interest.
- the general threshold-selection technique is illustrated in FIG. 8. The general technique was applied to a radiograph of human hands having the histogram shown in FIG. 9. The parameters were set as follows:
- the present invention provides a method for automatically detecting peaks in a gray level histogram of a digital image, and for selecting the gray level threshold values between distinguishable structures in the digital image.
- the method is useful in the field of digital image processing, particularly in the field of digital radiography.
- the method has the advantages that peaks are reliably detected in the presence of noise and gray level threshold values are selected automatically without the need for human intervention, thereby simplifying the digital image processing procedure making it more practical and useful.
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Abstract
Description
r(n)=F(n)-F.sub.w (n) (2)
r(n)=q.sub.w (n)*h(n)
q.sub.w (n)=d(n)*s.sub.w (n) (4)
______________________________________ STEP NO. ______________________________________ 0. j = 1 1.1. Compute .sup.--F.sub.w (n) with w = w.sub.j 1.2. Form r(n) = F(n) - .sup.--F.sub.w (n), or q.sub.w (n) * h(n) 1.3. Histogram peak detection: To detect peaks of the histogram consider the zeros and the local maxima of r(n). A zero-crossing to negative values indicates the start of a peak, i.e., the gray level at which the crossover occurs is a.sub.i. Similarly, the next zero-crossing to negative values at the gray level a.sub.i+1 (a.sub.i+1 >a.sub.i) indicates the start of the (i+1)th peak. The gray level b.sub.i, a.sub.i <b.sub.i <a.sub.i+1, at which r(b.sub.i) = Max [r(n)],a.sub.i < n < a.sub.i+1, determines the end point of the peak (see FIG. 5). That is, the ith peak is characterized by the pair (a.sub.i, b.sub.i), and the (i+1)th by (a.sub.i+1, b.sub.i+1) and so on. When the peak detection function has a negative value at n=o, it is assumed that the start of the first peak a.sub.1 is at zero. 1.4. Terminate the search for the peaks at the gray level n.sub.S. n.sub.S is determined from p(n.sub.Max -1) - P.sub.S = p(n.sub.s) (5) In other words, it is assumed that there does not exist a prominent detectable peak in the range where the upper P.sub.S percent (excluding the background level at n.sub.Max) of the gray levels are confined. The value of the parameter P.sub.S is determined empirically by studying various chest histograms. Note: If n.sub.s is reached after a zero-crossing to negative values but before the next zero-crossing to negative values, then the end point of the last peak (a.sub.K.sbsb.1, b.sub.K.sbsb.1) is taken to be n.sub.s i.e., b.sub.K.sbsb.1 = n.sub.s. At this point a set of peaks A defined by A .sup.Δ = {(a.sub.i, b.sub.i) : i = 1,2, . . . ,K.sub.1 } where 0 ≦ a.sub.i ≦ 2.sup.N - 1 and 0 ≦ b.sub.i ≦ 2.sup.N -1, is obtained. 1.5. Preprocessing: If a.sub.i+1 -b.sub.i < m, for any i = 1,2, . . . ,K.sub.1 -1 then (a.sub.i, b.sub.i) and (a.sub.i+1, b.sub.i+1) are combined into a single peak to form (a.sub.i, b.sub.i+1). In this case the set A becomes: A = {(a.sub.i, b.sub.i) : i=1,2, . . . K.sub.2 } (K.sub.2 ≦ K.sub.1). Parameter m is a constant that is determined experimentally. 1.6. Significance test: If the percentage of the gray levels confined to the peak (a.sub.i, b.sub.i), i = 1,2, . . . K.sub.2 is less than a certain value P.sub.sig, i.e., p(b.sub.i) - p(a.sub.i) < P.sub.sig, then the peak is considered to be insignificant and it is excluded from the set A. Thus for L (L ≧0) insignificant peaks A becomes: A = {(a.sub.i, b.sub.i) : i = 1,2, . . . K.sub.3 } where K.sub.3 = K.sub.2 - L P.sub.sig is a value that is determined experimentally. 1.7. Classification: the peaks are classified into clusters as follows: (a.sub.1, b.sub.1) belongs to the first cluster. (i) i = 2 (ii) IF (a.sub.i -b.sub.i-1 < d) THEN (a.sub.i, b.sub.i) and (a.sub.i-1, b.sub.i-1) belong to the same cluster ELSE (a.sub.i, b.sub.i) belongs to the next cluster; a.sub.i is the starting value of the next cluster, where d is a constant determined experimentally. (iii) i = i + 1 (iv) IF(i ≦ K.sub.3) GO TO (ii) STOP 1.8. Decision: threshold selection 1.8a. If the peaks are classified into two clusters then the lung/mediastinum threshold is set to a gray level n.sub.T which lies between the end point of the first cluster and the starting point of the second cluster, that is n.sub.T = int [μb(1) + (1-μ)a(2)], 0 ≦ μ ≦ 1, (6) where int[.] is the nearest integer truncation function, a(2) is the starting point of the second cluster, and b(1) is the end point of the first cluster. (Starting point of a cluster is defined to be the starting point of the first peak classified to that cluster. Similarly, end point of a cluster is defined to be the end point of the last peak classified to that cluster). 1.8b. If the peaks are classified into more than two clusters, the separation in gray levels between each successive clusters is computed. The pair with the largest separation is selected and the threshold is set to a gray level n.sub.T that lies between this pair, i.e., n.sub.T = int [μb(l) + (1-μ)a(l+1)], 0 ≦ μ ≦ 1, (7) where Max [a(x+1)-b(x)] = a(l+1) - b(l). x=1,2, . . . ,M (M is the total number of clusters). 1.8c. If only one peak is detected (K.sub.3 =1) IF (K.sub.3 =1) THEN IF ([p(n.sub.max -1) - p(b.sub.1)] < P.sub.T) THEN IF ( (j+1) ≦ J ) THEN w = w.sub.j+1 = (w.sub.j +1)/2 ! process can be repeated ! with a smaller window size GO TO STEP 1.1 ELSE Histogram is essentially unimodal. A threshold does not exist. END IF ELSE Histogram is essentially unimodal but a threshold can be set. n.sub.T = b.sub.1 END IF END IF Note: P.sub.T is an experimentally determined percentage criterium. J is a user specified parameter. 1.8d. If the peaks are classified into one cluster (M=1): IF ([p(n.sub.max -1) - p(b.sub.K.sbsb.3)] > P.sub.T) THEN n.sub.T = b.sub.K.sbsb.3 ELSE IF ( (j+1) ≦ J) THEN w = w.sub.j+1 = 2w.sub.j -1 ! process can be repeated ! with a larger window size GO TO STEP 1.1 ELSE Peaks are treated as clusters and decision is made according to (1.8b). END IF END IF ______________________________________
C={(e.sub.m,f.sub.m):m=1,2, . . . , M},
n.sub.T.sbsb.1,n.sub.T.sbsb.2, . . . , n.sub.T.sbsb.(M-1)
n.sub.T.sbsb.P =int{μf.sub.l +(1-μ)e.sub.l+1 },l=1,2 . . . , (M-1)
0≦μ≦1.
______________________________________ 2.1. i = 1 2.2. k = 1 2.3. IF (c.sub.k ≧ a.sub.i AND b.sub.i > d.sub.k) ! A.sub.2 -peak is contained (c.sub.k,d.sub.k) → (a.sub.i,b.sub.i) ! in the A.sub.1 -peak k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 END IF IF (c.sub.k ≦ a.sub.i AND d.sub.k ≧ b.sub.i) ! A.sub.1 -peak is contained a.sub.i = c.sub.k ! in the A.sub.2 -peak b.sub.i = d.sub.k ! replace the A.sub.1 -peak k = k + 1 ! with the A.sub.2 -peak IF (k > K) GO TO 2.7 GO TO 2.3 END IF 2.4. IF (c.sub.k ≦ a.sub.i ≦ d.sub.k) THEN ! (c.sub.k,d.sub.k) overlaps with ! (a.sub.i,b.sub.i) from left P.sub.k.sup.L = [P(d.sub.k)-p(a.sub.i)]/[p(d.sub.k)-p(c.sub.k)] ! left overlap percentage IF(P.sub.k.sup.L ≧ P.sub.L)THEN ! overlap signifi- cance ! check. P.sub.L is the left ! overlap signifi- cance ! measure (c.sub.k,d.sub.k) → (a.sub.i,b.sub.i) k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 ELSE (c.sub.k,d.sub.k) is independent k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 END IF END IF 2.5. IF (c.sub.k ≦ b.sub.i ≦ d.sub.k) THEN ! (c.sub.k,d.sub.k) overlaps with ! (a.sub.i,b.sub.i) from right P.sub.k.sup.R = [p(b.sub.i)-p(c.sub.k)]/[p(d.sub.k)-p(c.sub.k)] ! right overlap percentage IF (i < I) P.sub.k.sup.L = [p(d.sub.k)-p(a.sub.i+1)]/[p(d.sub.k)-p(c.sub.k )] ! check the possibility of ! left overlap with ! (a.sub.i+1,b.sub.i+1) IF (P.sub.k.sup.R ≧ P.sub.k.sup.L ) THEN ! right overlap IF (P.sub.k.sup.R ≧ P.sub.R) THEN ! overlap signifi- cance ! check. P.sub.R is the right ! overlap signifi- cance ! measure (c.sub.k,d.sub.k) → (a.sub.i,b.sub.i) k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 ELSE (c.sub.k,d.sub.k) is independent k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 END IF ELSE ! left overlap with (a.sub.i+1,b.sub.i+1) IF (P.sub.k.sup.L ≧ P.sub.L) THEN ! overlap signifi- cance check (c.sub.k,d.sub.k) → (a.sub.i+1,b.sub.i+1) k = k + 1 i = i + 1 IF (k > K) GO TO 2.7 GO TO 2.3 ELSE (c.sub.k,d.sub.k) is independent k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 END IF END IF END IF 2.6. IF (d.sub.k < a.sub.i) THEN ! (c.sub.k,d.sub.k) lies to the left of (c.sub.k,d.sub.k) is independent ! (a.sub.i,b.sub.i) with no overlap k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 ELSE ! (c.sub.k,d.sub.k) lies to the right of ! (a.sub.i,b.sub.i) with no overlap IF (i ≧ I) THEN ! it lies to the right of the ! last A.sub.1 -peak (c.sub.k,d.sub.k) is independent k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 END IF DO LL = i + 1, I ! check for possible overlaps ! with upcoming A.sub.1 -peaks IF (a.sub.LL ≦ d.sub.k ≦ b.sub.LL) THEN ! an overlap exists i = LL GO TO 2.3 ELSE CONTINUE END IF ENDDO (c.sub.k,d.sub.k) is independent ! no overlap k = k + 1 IF (k > K) GO TO 2.7 GO TO 2.3 END IF Note: P.sub.L and R.sub.R are the left and the right overlap significance criteria respectively. P.sub.L = P.sub.R = P.sub.O without loss of generality. P.sub.O is determined heuristically. 2.7. A.sub.1 -peaks that either do not overlap with any of the A.sub.2 -peaks or overlap with A.sub.2 -peaks insignificantly are independent peaks. STOP ______________________________________
A.sub.1 ={(0,1385),(1484,2319),(2436,2902)}(w.sub.1 =541)
A.sub.2 ={(509,1385),(1496,1744),(1785,2006),(2014,2303),(2428,2623),(2662,2902)}(w.sub.2 =271).
C={(509,1385),(1496,2006),(2014,2303),(2428,2623),(2662,2902)}.
Claims (6)
q.sub.w (n)=d(n)*s.sub.w (n)
Priority Applications (5)
Application Number | Priority Date | Filing Date | Title |
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US06/848,509 US4731863A (en) | 1986-04-07 | 1986-04-07 | Digital image processing method employing histogram peak detection |
EP87902953A EP0301028B1 (en) | 1986-04-07 | 1987-03-27 | A method for automatically detecting peaks in the gray-level histogram of a digital image |
JP62502619A JPH01502463A (en) | 1986-04-07 | 1987-03-27 | A method for automatically detecting peaks in gray level histograms of digital images |
DE8787902953T DE3780955T2 (en) | 1986-04-07 | 1987-03-27 | METHOD FOR AUTOMATIC PEAK DETECTION IN THE GRAY-GRADE HISTOGRAM OF A DIGITAL IMAGE. |
PCT/US1987/000656 WO1987006374A1 (en) | 1986-04-07 | 1987-03-27 | A method for automatically detecting peaks in the gray-level histogram of a digital image |
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US06/848,509 US4731863A (en) | 1986-04-07 | 1986-04-07 | Digital image processing method employing histogram peak detection |
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US06/848,509 Expired - Lifetime US4731863A (en) | 1986-04-07 | 1986-04-07 | Digital image processing method employing histogram peak detection |
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US5247154A (en) * | 1991-01-17 | 1993-09-21 | Westinghouse Electric Corp. | Method and apparatus for monitoring the laser marking of a bar code label |
US5268967A (en) * | 1992-06-29 | 1993-12-07 | Eastman Kodak Company | Method for automatic foreground and background detection in digital radiographic images |
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Also Published As
Publication number | Publication date |
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DE3780955D1 (en) | 1992-09-10 |
EP0301028A1 (en) | 1989-02-01 |
DE3780955T2 (en) | 1993-04-15 |
WO1987006374A1 (en) | 1987-10-22 |
EP0301028B1 (en) | 1992-08-05 |
JPH01502463A (en) | 1989-08-24 |
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